Let P: R 3 → R 3 be the projection onto the plane x + y − z = 0. a) Prove that P is linear. [2] b) Prove that P o P = P. [2] c) Find bases for the subspaces Null(P) and Range(P). [2] d) Find the s

Let P: R 3 → R 3 be the projection onto the plane x + y − z = 0.

a) Prove that P is linear. [2]

b) Prove that P o P = P. [2]

c) Find bases for the subspaces Null(P) and Range(P). [2]

d) Find the standard matrix A of P and show that A^2 = A and A = A^T. [2]